In this talk we consider the SL(2,C)-character variety X=Hom(F_3, SL(2,C))//SL(2,C) of the free group F_3 of rank 3. We will consider F_3 as the fundamental group of two different surfaces: the four-holed sphere S, and of the three-holed punctured plane N. We will consider the action of the mapping class groups MCG(S) and MCG(N) on it. In particular, we describe a domain of discontinuity for these actions on the relative character varieties X_rel(S) and X_rel(N), which are the set of representations for which the traces of the boundary curves are fixed. Time permitting, we will mention some open questions on which we are working on now.

(Part of this is joint work with F. Palesi and S. P. Tan, and part is work in progress with F. Palesi.)